4,761 research outputs found
A parameter robust numerical method for a two dimensional reaction-diffusion problem.
In this paper a singularly perturbed reaction-diffusion partial differential equation in two space dimensions is examined. By means of an appropriate decomposition, we describe the asymptotic behaviour of the solution of problems of this kind. A central finite difference scheme is constructed for this problem which involves an appropriate Shishkin mesh. We prove that the numerical approximations are almost second order uniformly convergent (in the maximum norm) with respect to the singular perturbation parameter. Some numerical experiments are given that illustrate in practice the theoretical order of convergence established for the numerical method
Exact phase space functional for two-body systems
The determination of the two-body density functional from its one-body
density is achieved for Moshinsky's harmonium model, using a phase-space
formulation, thereby resolving its phase dilemma. The corresponding sign rules
can equivalently be obtained by minimizing the ground-state energy.Comment: Latex, 12 page
A Renormalization Group Analysis of the NCG constraints m_{top} = 2\,m_W},
We study the evolution under the renormalization group of the restrictions on
the parameters of the standard model coming from Non-Commutative Geometry,
namely and . We adopt the point of
view that these relations are to be interpreted as {\it tree level} constraints
and, as such, can be implemented in a mass independent renormalization scheme
only at a given energy scale . We show that the physical predictions on
the top and Higgs masses depend weakly on .Comment: 7 pages, FTUAM-94/2, uses harvma
Fourier analysis on the affine group, quantization and noncompact Connes geometries
We find the Stratonovich-Weyl quantizer for the nonunimodular affine group of
the line. A noncommutative product of functions on the half-plane, underlying a
noncompact spectral triple in the sense of Connes, is obtained from it. The
corresponding Wigner functions reproduce the time-frequency distributions of
signal processing. The same construction leads to scalar Fourier
transformations on the affine group, simplifying and extending the Fourier
transformation proposed by Kirillov.Comment: 37 pages, Latex, uses TikZ package to draw 3 figures. Two new
subsections, main results unchange
The Kirillov picture for the Wigner particle
We discuss the Kirillov method for massless Wigner particles, usually
(mis)named "continuous spin" or "infinite spin" particles. These appear in
Wigner's classification of the unitary representations of the Poincar\'e group,
labelled by elements of the enveloping algebra of the Poincar\'e Lie algebra.
Now, the coadjoint orbit procedure introduced by Kirillov is a prelude to
quantization. Here we exhibit for those particles the classical Casimir
functions on phase space, in parallel to quantum representation theory. A good
set of position coordinates are identified on the coadjoint orbits of the
Wigner particles; the stabilizer subgroups and the symplectic structures of
these orbits are also described.Comment: 19 pages; v2: updated to coincide with published versio
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